Complex diseases, such as coronary heart disease, diabetes, and Alzheimer's disease, are those which, while having a genetic component, do not display classical Mendelian inheritance patterns. This is thought to be due to such diseases being controlled by multiple, possibly interacting, genetic and environmental factors. Linkage analysis is a powerful technique for locating disease genes. The computational costs of linkage calculations increase rapidly with the number of marker loci, the size and complexity of pedigrees, and the complexity of the trait model. For this reason, linkage analyses are commonly performed on small pedigrees or with a small number of markers, despite evidence that using more loci and larger pedigrees can increase power. In addition, simple traits models are often used even when they are thought to be inappropriate. Markov chain Monte Carlo (MCMC) methods offer a solution to these problems by using a sampling based approach to linkage calculations which is less computationally intensive than conventional approaches. MCMC methodology can be used to extend the range of linkage analyses that are possible, and thereby increase the power to locate genes affecting complex diseases. The specific aims of this proposal are: (1) Improving the sampling efficiency of MCMC samplers for pedigree data. Effective samplers for tightly linked loci and a range of pedigree types from nuclear families to large complex pedigrees will be developed. Practical diagnostic tests for the samplers will also be developed; (2) Developing methods for detecting and allowing for errors in genetic data and linkage maps, leading to more robust methods of linkage analysis; (3) Investigating the information contained in complex pedigree structures by examining the effect of simplifying pedigrees on the ability to detect trait loci; (4) Developing methods for linkage analysis using complex trait models with multiple interacting genetic and environmental factors. Methods for checking the fit of models to data will also be investigated.